On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case

Shiqiu Zheng () and Shoumei Li ()
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Shiqiu Zheng: Beijing University of Technology
Shoumei Li: Beijing University of Technology

Journal of Theoretical Probability, 2018, vol. 31, issue 1, 119-158

Abstract: Abstract A system of dynamically consistent nonlinear evaluation ( $${\mathcal {F}}$$ F -evaluation) provides an ideal characterization for the dynamical behaviors of risk measures and the pricing of contingent claims. The purpose of this paper is to study the representation for the $${\mathcal {F}}$$ F -evaluation by the solution of a backward stochastic differential equation (BSDE). Under a general domination condition, we prove that any $${\mathcal {F}}$$ F -evaluation can be represented by the solution of a BSDE with a generator which is Lipschitz in y and uniformly continuous in z.

Keywords: Backward stochastic differential equation; g-expectation; g-evaluation; Nonlinear expectation; Nonlinear evaluation; 60H10 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0705-5

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